The U.S. Justice Department on Monday launched its case for a higher estimate of how much oil coursed out of the Macondo well in 2010, and BP lawyers began working to pick apart the federal government's experts and their theories on the epic Gulf of Mexico oil spill, all with potentially billions of dollars in fine money at stake, in the latest round of the BP trial in federal court in New Orleans.

The Justice Department says 4.2 million barrels emptied into the Gulf during the course of the spill. BP says it was 2.45 million barrels. Settling on a number will be key in determining any fines U.S. District Judge Carl Barbier might impose on BP if he finds negligence on the part of the company, because federal law outlines a per-barrel system of penalizing pollution from oil spills. At the high end, the range of possible fines spans $2.7 billion to $18 billion. But Barbier also could issue lower fines.

After opening statements, the trial spent much of the day on testimony from Ronald Dykhuizen, an engineering and fluids expert from Sandia National Laboratories, a major Energy Department lab, who joined the oil spill response in 2010.

Dykhuizen examined data on how much oil pulsed through the capping stack device that eventually stopped the gusher, arriving at a range of 43,000 barrels to 63,000 barrels per day at the end of the ordeal and about 53,000 barrels a day as the best estimate.

He called the calculations "standard equations you find in a first-year undergraduate course," he said.

He also looked at pressure in the failed blowout preventer tower on the sea floor as BP tried the "top kill" strategy for quieting the well by pumping in heavy drilling mud and bits of debris to counteract the force of the surging oil, and on that basis, he came up with a range of 44,000 to 77,000 barrels spilled per day. And he measured oil based on how much BP collected when it lowered a "top hat" device, described as an upside-down funnel, to capture some oil as it was still leaking, again reaching similar ranges.

Under questioning by Justice Department lawyer Scott Cernich, Dykhuizen described what he saw as shortcomings in other experts' methods.

On cross-examination, BP lawyer Matt Regan singled out his uncertainty ranges of 20 percent to 30 percent up or down, getting Dykhuizen to agree that his estimates are not pinpoint accurate.

But while answering questions from Cernich, Dykhuizen said his idea of inaccuracy is anything outside a 1 percent error range. "I like to think that my estimates are reliable, but in any model of any system, estimates have a certain uncertainty to it," Dykhuizen said. "I think this is still an informative calculation. It was the best I could do with the data that I had."

Monday began with Steve O'Rourke, lawyer for the federal government, outlining estimates that 62,000 barrels of oil poured into the Gulf each day at the beginning of the spill in April 2010, dropping to 53,000 barrels by the end of the crisis in July 2010 as pressure dropped in the emptying Macondo well.

"They will nitpick our experts, for sure, but they are not going to tell you what the flow rate was," O'Rourke said, anticipating BP's case.

He said his witnesses will refute BP efforts to suggest that government estimates were politically driven.

While BP will try to poke holes in the models from the government's experts, O'Rourke said, "Between BP's own experts, there's a 25 percent difference."

O'Rourke said the government will present estimates based on four different methods of measuring the deep-sea oil gusher. The methods include using pressure data from the capping stack, using data from the blowout preventer, examining geological characteristics of the well and using several data points to simulate the size of the oil reservoir.

Oil gushes out of the blowout preventer atop the BP Macando well in the Gulf of Mexico in July 2010.BP

To illustrate various points, he employed analogies ranging from deflating vehicle tires to Champagne corks to garden hoses and even oil-saturated faces of acne-prone teenaged boys. On that last one, he was referring to oil-soaked stone under the sea floor. That relates to a key concept in this part of the trial, called rock compressibility, or the degree to which rocks in the reservoir held oil and influenced the pressure for it to erupt upward in the blowout.

When factoring out more than 800,000 barrels BP captured during the "top hat" operation, O'Rourke said, the amount of oil that escaped into the Gulf equaled 16 Exxon Valdez tankers, referring to the Alaskan oil spill in 1989.

He argued, meanwhile, that BP ignores data from the three months after the spill in reaching its own estimate.

A BP lawyer, Mike Brock, expressed the flip side of that point in his opening statement, saying it's better to use calculations on the total contents of the underground oil reservoir before and after the spill than to try gauging points in between when conditions of the well were changing.

"There are changes in the Macondo well that are occurring daily," during the spill, Brock said.

Sand pumping through the well and eroding equipment meant that the force of the flow increased over time as obstructions were ground down, Brock said, presenting a view opposite from the government's contention that the torrent slowed as the reservoir of oil decreased.

"In order for the government models to work," Brock said, "they have to explain away erosion in the well as having all occurred in the first few hours, and the evidence is going to be contrary to that."

He said BP's experts could avoid the complications of measuring what poured out during the event by using pressure readings and fluid samples from the well before the blowout and after it was capped.

"This information is relied on in the industry to help make predictions about the well, assuming that it's successfully drilled," Brock said. "These are not figures that BP has come up with after the fact."

Brock also presented emails and notes from meetings of government officials talking about being under pressure to release new estimates of the size of the spill in late July and early August of 2010, even when a full analysis was not ready.

Among the lines from an official in the emails: "He said that we HAVE to have a new flow rate by FRIDAY. He said that is coming from Secretary Chu and above," referring to then-Energy Secretary Steven Chu.

The government's first witness on Monday, Thomas Hunter, former director of Sandia National Laboratories and a leader of the government's scientific team that responded to the spill, faced questions about his emails on getting pressed for time to produce numbers, but described the work as unfolding gradually and not rushed.

Brock also introduced video testimony of government experts, such as Dykhuizen, talking about ranges of error in their reports. "The government has not accounted for the events within the well on a day-by-day basis," Brock said.

He said BP's experts will explain why that's a problem, in part describing holes and leaks in the riser pipe that popped up with sand erosion over time, a factor government experts downplay.

Hunter, the first government witness, testified that the existence of erosion in the equipment on its own wasn't enough to seriously alter the results: "It would be critical that erosion occur in a place that was blocking the flow, and that's not known."

Brock said BP's witnesses also will explain the appearance of "slugs" in the piping where clots of oil pumped out intermittently with clouds of gas, also giving different indications from the government's about how much was escaping.

"Our position is we should pay for what happened realistically in terms of the outcome," he said.

This is the second part of the second phase of the trial, and it is expected to last three weeks. In the first phase in the spring, the trial looked at what caused the Deepwater Horizon rig explosion and Macondo well blowout and how it could have been prevented. Last week at the start of phase two, the trial scrutinized BP's efforts to stop the gusher once it had started.